Problem: Simplify the expression. $ (3z^{6}-z^{3}+z) - ( 6z^{6}-7z^{3}) $
Solution: Distribute any negative signs. $(3z^{6}-z^{3}+z) + (-6z^{6}+7z^{3})$ Since we are adding polynomials, we can simply remove the parentheses. $3z^{6}-z^{3}+z - 6z^{6}+7z^{3}$ Identify like terms. $ {3 z^6} - \color{#DF0030}{ z^3} + { z} - {6 z^6} + \color{#DF0030}{7 z^3} $ Combine like terms. $ { ( 3 -6 ) z^6} + \color{#DF0030}{ z^3} + { z} $ Add the coefficients. $-3z^{6}+6z^{3}+z$